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Even and odd atomic nuclei
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<p>In <a href="/facts/Nuclear_physics/fzQbt1aF">nuclear physics</a>, properties of a <a href="/facts/Atomic_nucleus/orpIm5Xl">nucleus</a> depend on <a href="/facts/Even_and_odd_numbers/7zq2UM4V">evenness or oddness</a> of its <a href="/facts/Atomic_number/bgAr581S">atomic number</a> (proton number) <i>Z</i>, <a href="/facts/Neutron_number/eNtwGnVL">neutron number</a> <i>N</i> and, consequently, of their sum, the <a href="/facts/Mass_number/VyBbJ1oI">mass number</a> <i>A</i>. Most importantly, oddness of both <i>Z</i> and <i>N</i> tends to lower the <a href="/facts/Nuclear_binding_energy/PU8bREHW">nuclear binding energy</a>, making odd nuclei generally less stable. This effect is not only experimentally observed, but is included in the <a href="/facts/Semi-empirical_mass_formula/XQhTYz7e">semi-empirical mass formula</a> and explained by some other <a href="/facts/Nuclear_model/orpIm5Xl">nuclear models</a>, such as the <a href="/facts/Nuclear_shell_model/1Qgep495">nuclear shell model</a>. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-<i>A</i> <a href="/facts/Isobar_(nuclide)/25ezJVsq">isobars</a>, has important consequences for <a href="/facts/Beta_decay/vxTBlckp">beta decay</a>. </p><p>The <a href="/facts/Nuclear_spin/1Qgep495">nuclear spin</a> is zero for even-Z, even-N nuclei, integer for all even-<i>A</i> nuclei, and odd half-integer for all odd-<i>A</i> nuclei. </p> Even vs. odd mass number (<i>A</i>).<table><tbody><tr><th></th><th>Even</th><th>Odd</th><th>Total</th></tr><tr><td>Stable</td><td>150</td><td>101</td><td>251</td></tr><tr><td><a href="/facts/Primordial_nuclide/lFAUqHDv">Long-lived</a></td><td>26</td><td>9</td><td>35</td></tr><tr><td>All <a href="/facts/Primordial_nuclide/lFAUqHDv">primordial</a></td><td>176</td><td>110</td><td>286</td></tr></tbody></table> <p>The <a href="/facts/Neutron%E2%80%93proton_ratio/qB9ICUHF">neutron–proton ratio</a> is not the only factor affecting nuclear stability. Adding neutrons to isotopes can vary their nuclear spins and nuclear shapes, causing differences in <a href="/facts/Neutron_capture/elsFpM12">neutron capture</a> <a href="/facts/Cross_section_(physics)/lo014h2D">cross sections</a> and <a href="/facts/Gamma_spectroscopy/sSsWI23T">gamma spectroscopy</a> and <a href="/facts/Nuclear_magnetic_resonance/pGYAn9Bz">nuclear magnetic resonance</a> properties. If too many or too few neutrons are present with regard to the <a href="/facts/Nuclear_binding_energy/PU8bREHW">nuclear binding energy</a> optimum, the nucleus becomes unstable and subject to certain types of <a href="/facts/Nuclear_decay/Ya6FVjt4">nuclear decay</a>. Unstable nuclides with a nonoptimal number of neutrons or protons decay by <a href="/facts/Beta_decay/vxTBlckp">beta decay</a> (including positron decay), <a href="/facts/Electron_capture/EIccoV1u">electron capture</a>, or other means, such as <a href="/facts/Spontaneous_fission/0QuJoVKI">spontaneous fission</a> and <a href="/facts/Cluster_decay/sIelGo3t">cluster decay</a>. </p>